Highest Common Factor of 462, 196, 71 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 462, 196, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 462, 196, 71 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 462, 196, 71 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 462, 196, 71 is 1.
HCF(462, 196, 71) = 1
HCF of 462, 196, 71 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 462, 196, 71 is 1.
Highest Common Factor of 462,196,71 is 1
Step 1: Since 462 > 196, we apply the division lemma to 462 and 196, to get
462 = 196 x 2 + 70
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 70 and 196, to get
196 = 70 x 2 + 56
Step 3: We consider the new divisor 70 and the new remainder 56, and apply the division lemma to get
70 = 56 x 1 + 14
We consider the new divisor 56 and the new remainder 14, and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 462 and 196 is 14
Notice that 14 = HCF(56,14) = HCF(70,56) = HCF(196,70) = HCF(462,196) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71 > 14, we apply the division lemma to 71 and 14, to get
71 = 14 x 5 + 1
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 1 and 14, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 71 is 1
Notice that 1 = HCF(14,1) = HCF(71,14) .
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Frequently Asked Questions on HCF of 462, 196, 71 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 462, 196, 71?
Answer: HCF of 462, 196, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 462, 196, 71 using Euclid's Algorithm?
Answer: For arbitrary numbers 462, 196, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.